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Free After Execution (フリー・アフター・エグゼキューション) is abbreviated as FAE, is not a magic but a theory describing one peculiarity of the interaction between magic and the physical world.
“In Japanese, it is called the theory of controlling phenomenon after it had been created but Free After Execution is a better way of expressing it. The phenomenon produced as a result being transformed by magic is already a phenomenon that was not originally in this world, immediately after transformation the shackles of the laws of physics are loose. Perhaps it would be better if I changed it to a short time lag exists between when the laws of physics reasserts itself after an event produced by magic.”
As it is explained by Shiba Tatsuya in Visitor Arc, Chapter 13, there is a tiny time-gap between the end of a magic effect changing reality and laws of physics retaking control of reality. However, if someone manages to exploit this loophole, it is possible to achieve otherwise hardly achievable results.
FAE, although it was originally a joint research between Japan and the USNA, was only developed by the latter into a practical application. It is suggested that the original program was a secret research that was expropriated by the USNA. Brionac, the Specialized CAD Major Angie Sirius uses, is the product of this research. It is the tool capable of transforming the Strategic-Class Magic Heavy Metal Burst into a practical tactical weapon.
Later Tatsuya developed a new magic called Baryon Lance which also exploits the possibilities of the theory.